Shapes of s, p and d Orbitals (Spherical, Dumbbell and More)

Chemistry · Structure Of Atom · NEET

An s orbital is a simple sphere (a ball) around the nucleus. A p orbital looks like a dumbbell, with two lobes on opposite sides. Most d orbitals have four lobes (like a clover). Memory hook: S = Sphere, P = Peanut (dumbbell), D = Double-dumbbell (four lobes).
Shapes of s, p and d Orbitalss orbital (l=0)Sphere (1 part)p orbital (l=1)Dumbbell (2 lobes)d orbital (l=2)Four lobes (clover)l decides shape: 0 to sphere, 1 to dumbbell, 2 to four lobes
The azimuthal quantum number l fixes the shape: l=0 gives a spherical s orbital, l=1 gives a dumbbell-shaped p orbital (2 lobes), and l=2 gives a four-lobed d orbital. Number of lobes grows as l increases.

Your doubts, answered

What is the shape of s, p and d orbitals in simple words?

An s orbital is spherical (a round ball around the nucleus). A p orbital is dumbbell-shaped: two lobes on opposite sides of the nucleus, with a gap in the middle where the electron is never found. A d orbital normally has four lobes (a double-dumbbell or clover shape). The shape is decided by the azimuthal quantum number l: l=0 gives s (sphere), l=1 gives p (dumbbell), l=2 gives d (four lobes). For NEET, remember l decides the SHAPE.

Why is the s orbital spherical but the p orbital dumbbell-shaped?

An s orbital has l=0, so it has no angular node (no flat plane where the electron is missing). This makes the chance of finding the electron the same in every direction, which gives a sphere. A p orbital has l=1, so it has one angular node (a flat plane through the nucleus). On that plane the chance of finding the electron is zero, so the shape breaks into two lobes on either side, giving a dumbbell. More angular nodes means a shape with more lobes.

Which d orbitals have lobes along the axes and which lie between the axes?

There are five d orbitals. Two of them, d(z²) and d(x²-y²), have their lobes pointing ALONG the x, y, z axes (this pair is called the e_g set). The other three, d(xy), d(yz) and d(xz), have their lobes lying BETWEEN the axes (this trio is called the t_2g set). NEET 2016 asked exactly this: the pair with electron density along the axes is d(z²) and d(x²-y²).

Why does the d(z²) orbital look different (a doughnut in the middle)?

Four of the five d orbitals have the same clover shape (four lobes), just pointing in different directions. The d(z²) orbital is the odd one out: it has two big lobes along the z-axis plus a small doughnut-shaped ring (a torus) around the middle in the xy-plane. Its shape looks different but it still belongs to the same set of five d orbitals with equal energy. Its magnetic quantum number m is 0.

Does the shape tell the real path of the electron?

No. The shape is only a boundary surface: the region where there is about a 90 percent chance of finding the electron. An orbital is NOT a fixed path like a Bohr orbit. Because of Heisenberg's uncertainty principle, we cannot know the exact path. The shape just shows where the electron is most likely to be, based on ψ² (probability density).

How many nodes and lobes does each orbital have?

An s orbital has 0 angular nodes and no lobes (it is one sphere). A p orbital has 1 angular node and 2 lobes (dumbbell). A d orbital has 2 angular nodes and usually 4 lobes. The number of angular nodes equals l. For NEET, angular nodes = l, so s=0, p=1, d=2, f=3.

⚠️ The NEET trap
All five d orbitals have their lobes lying between the axes.
Only three d orbitals (d(xy), d(yz), d(xz)) lie between the axes. The other two, d(z²) and d(x²-y²), point ALONG the axes.
🧠 Squared names point straight: d(z²) and d(x²-y²) both have a 'square' in the name and both point ALONG the axes.

Real NEET questions

NEET 2016

Which of the following pairs of d-orbitals will have electron density along the axes?

A · d(z²), d(xz)
B · d(xz), d(yz)
C · d(z²), d(x²-y²)
D · d(xy), d(x²-y²)
Solution: d(z²) and d(x²-y²) form the e_g set. Their lobes point ALONG the cartesian axes. The other three orbitals d(xy), d(yz), d(xz) (the t_2g set) have their lobes lying BETWEEN the axes. So the pair with electron density along the axes is d(z²) and d(x²-y²).
NEET 2024

Match List-I (Quantum Number) with List-II (Information provided). (A) m_l (B) m_s (C) l (D) n. List-II: (I) shape of orbital, (II) size of orbital, (III) orientation of orbital, (IV) orientation of spin of electrons.

A · A-III, B-IV, C-I, D-II
B · A-III, B-IV, C-II, D-I
C · A-II, B-I, C-IV, D-III
D · A-I, B-III, C-II, D-IV
Solution: The magnetic quantum number m_l gives the orientation of the orbital (III). m_s gives the orientation of electron spin (IV). The azimuthal quantum number l decides the SHAPE of the orbital (I). The principal quantum number n gives the size (II). So A-III, B-IV, C-I, D-II. Key point for shapes: it is l, not n, that fixes the shape.
NEET 2017 · 2018

Which one is a wrong statement?

A · Electronic configuration of N atom is 1s² 2s² 2p_x¹ 2p_y¹ 2p_z¹
B · An orbital is designated by three quantum numbers while an electron in an atom is designated by four quantum numbers
C · Total orbital angular momentum of an electron in an s orbital is equal to zero
D · The value of m for d(z²) is zero
Solution: Per the official key, statement (A) is treated as the wrong option here. The other statements are all correct and useful for shapes: an orbital needs three quantum numbers (n, l, m_l); for an s orbital l=0 so its orbital angular momentum √(l(l+1))·h/2π = 0; and for the d(z²) orbital the magnetic quantum number m = 0.

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Frequently asked

Which quantum number decides the shape of an orbital?

The azimuthal quantum number l decides the shape. l=0 gives a spherical s orbital, l=1 gives a dumbbell p orbital, and l=2 gives a four-lobed d orbital. The principal quantum number n decides size, and m_l decides orientation.

How many p and d orbitals are there in a subshell?

There are three p orbitals (p_x, p_y, p_z) and five d orbitals (d(xy), d(yz), d(xz), d(x²-y²), d(z²)) in each subshell. The number of orbitals equals 2l+1.

Do all s orbitals (1s, 2s, 3s) have the same shape?

Yes, all s orbitals are spherical. But the size grows with n, so 4s > 3s > 2s > 1s. Higher s orbitals also have more radial nodes inside, but the outer boundary shape stays a sphere.

What is the difference between d(z²) and the other d orbitals?

Four d orbitals have the same four-lobe clover shape. The d(z²) orbital is special: it has two lobes along the z-axis plus a doughnut-shaped ring around the centre. All five still have equal energy in a free atom.

Is an orbital shape the same as an electron's path?

No. A shape is just the region where the electron is very likely to be (about 90 percent chance). It is not a fixed path. By Heisenberg's uncertainty principle, the exact path of an electron cannot be known.